MHB How Do You Convert Temperatures and Solve Inverse Functions?

AI Thread Summary
Temperatures can be converted from Fahrenheit to Celsius using the function f(x) = 5/9(x − 32). The calculation for f(59) results in 15 degrees Celsius. To find the inverse function f^(-1)(x), one must rearrange the equation y = 5/9(x − 32) to express x in terms of y. Additionally, the set K, defined as {x : f(x) = x}, requires solving the equation 5/9(x − 32) = x to identify its elements. This discussion emphasizes the importance of understanding function inverses and solving equations in temperature conversion.
charlottecain
Messages
1
Reaction score
0
Temperatures can be converted from Fahrenheit to Celsius using the
function f(x) = 5
/9
(x − 32).
(a) Calculate f(59).
(b) Find f
−1
(x), and verify that f
−1
(f(59)) = 59.
(c) Let K be the set {x : f(x) = x}. Find all elements of K and list K
 
Mathematics news on Phys.org
Hi, and welcome to the forum!
charlottecain said:
Temperatures can be converted from Fahrenheit to Celsius using the
function $f(x) = \frac59(x − 32)$.
(a) Calculate $f(59)$.
\[
f(59)=\frac59(59-32)=\frac59\cdot27=5\cdot\frac{27}{9}=5\cdot 3=15.
\]

charlottecain said:
(b) Find $f^{-1}(x)$, and verify that $f^{-1}(f(59)) = 59$.
To find the inverse of $f$ you need to solve the equation $y=\frac59(x − 32)$ for $x$, i.e., express $x$ through $y$. Can you do this? Start by multiplying both sides by $\frac95$.

charlottecain said:
(c) Let K be the set {x : f(x) = x}. Find all elements of K and list K
To do this you need to solve the equation $\frac59(x − 32)=x$. Can you do this?

For the future, please review the http://mathhelpboards.com/rules/, especially rule #11 (please click the "Expand" button in the top-left corner).
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top